Question

1. if $p\\$q$ is defined as $p\\$q = p^2 - 2q + 3$, evaluate $2\\$5$.

a. $-3$
b. $-9$
c. $11$
d. $5$

Explanation:

Step1: Identify p and q

Here, \( p = 2 \) and \( q = 5 \) for the operation \( p\$q \).

Step2: Substitute into the formula

Substitute \( p = 2 \) and \( q = 5 \) into \( p\$q = p^2 - 2q + 3 \).
We get \( 2^2 - 2\times5 + 3 \).

Step3: Calculate each term

First, \( 2^2 = 4 \), \( 2\times5 = 10 \).
So the expression becomes \( 4 - 10 + 3 \).

Step4: Perform the arithmetic

\( 4 - 10 = -6 \), then \( -6 + 3 = -3 \). Wait, no, wait: Wait, 4 - 10 is -6, then -6 + 3 is -3? But let's check again. Wait, 2 squared is 4, minus 2 times 5 (which is 10) plus 3. So 4 - 10 is -6, plus 3 is -3? But let's check the options. Option A is -3. Wait, but let's recalculate:

Wait, \( p = 2 \), \( q = 5 \). So \( p^2 = 4 \), \( 2q = 10 \). So \( 4 - 10 + 3 = (4 + 3) - 10 = 7 - 10 = -3 \). Yes, that's correct.

Answer:

A. -3